First, we need to calculate the weight of the hot air balloon:
Weight = Mass x Gravity
Weight = 450 kg x 9.81 m/s^2
Weight = 4414.5 N
Next, we need to calculate the volume of the air displaced by the hot air balloon:
V = Weight / (Density outside - Density inside)
V = 4414.5 N / (1.29 kg/m^3 - 0.90 kg/m^3)
V = 4414.5 N / 0.39 kg/m^3
V = 11324.36 m^3
Therefore, the envelope must expand to a volume of 11324.36 m^3 in order to lift the balloon into the air.
A hot air balloon including the envelope, gondola, burner and fuel and one passenger has a total mass of 450 kg. The air outside the balloon at 200C and has a density of 1.29 kg/m3. The air inside the envelope is heated to a temperature of 1200C, at which it has a density of 0.90 kg/m3. What volume must the envelope expand in order to lift the balloon into the air?
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